twenty twelve header background image

the bg at the part where the name of the side and the short description is .. between the menu bar and the grey border at the top.

Are you trying to set up a header image ?

If that’s the case, you could do so under Appearance > Header

I’m not sure where exactly you want that pic to be placed at.

Suppose you want that pic to replace the site’s title and site’s description, then read on.

First create a child theme
http://codex.wordpress.org/Child_Themes

or dl a blank one from here
http://quirm.net/themes/twenty-twelve-child/

We will make modifications in child theme only, after you have child theme installed and activated properly, copy over the header.php from parent theme and add this one line of code

<img class="header-image" src="http://www.earthpix.eu/data/header.jpg" alt="earthpix.eu" />

Just below the <header> tag

So you will have this, notice the <img> just below <header>

<header id="masthead" class="site-header" role="banner">
		<img class="header-image" src="http://www.earthpix.eu/data/header.jpg" alt="earthpix.eu" />
		<hgroup>

Then go over the Appearance > Header and set it not to display site title text.